I would submit that Early Modern is vastly more accessible than Middle English - it sounds an awful lot like a strong Northeast Kingdom accent - and that it would be far more accessible than people might fear. I think the issue with Shakespearean English is that it wouldn't interfere with comprehension but would still just be a novelty to the audience and not really worth the time and effort involved in getting the actors to acquire it. Geekery still, but perhaps not quite so rarified.